It is shown that a single-walled carbon nanotube based on a carbon monolayer (graphene) rolled up into a cylinder is a nanoscale quantum system characterized by the presence of electron crystals, like graphene. In contrast to the extremely unstable graphene quantum system, the nanotube quantum system is stable at a certain curvature of the carbon skeleton. The curvature causes the redistribution of π electrons between internal and external electron crystals accompanied by the formation of additional one-dimensional or quasi-onedimensional crystals of pairs of π* electrons excited into a higher 3s2pz energy state and located on the nanotube external side. The stability of the nanotube quantum system and its unusual physical properties are due to these crystals of π* electron pairs.